Balanced subgroups of totally projective groups
type: Item
instance of: scholarly article
title: Balanced subgroups of totally projective groups
zbMATH Open document ID: 0545.20043
DOI: 10.1016/0021-8693(84)90069-3
author: P. Hill
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: \textit{F. Richman} and \textit{E. Walker} showed that balanced subgroups of totally projective groups are not necessarily totally projective [J. Algebra 56, 145-167 (1979; Zbl 0401.20049)]. Nevertheless, the author proves the following remarkable theorem: Let B and B' be balanced subgroups of reduced totally projective p-groups A and A', respectively. If B and B' have the same Ulm-Kaplansky invariants and if A/\(B\cong A'/B'\), then B and B' are isomorphic. Moreover, there is an isomorphism from A onto A' which maps B onto B'.
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 20K99
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K40
zbMATH DE Number: 3867590
zbMATH Keywords: balanced subgroups
zbMATH Keywords: reduced totally projective p-groups
zbMATH Keywords: Ulm-Kaplansky invariants
reviewed by: K.-y.Honda
MaRDI profile type: Publication
full work available at URL: 0021-8693(84)90069-3
OpenAlex ID: W2086195899
cites work: Note on extensions of Abelian groups by primary groups
cites work: Extensions of Free Groups by Torsion Groups
cites work: Valuated groups
description: scientific article; zbMATH DE number 3867590